I get what you're saying but in this case folding would still be bat****.

Where did you get this read? The op said nothing of the button's opening frequency. I don't think opening any two cards on the button is good poker no matter the number of opponents. Then you expect him to call the flop with **** like T2s? I wouldn't be surprised if a good button calling range was <60% of all hands on the flop. So I'm inclined to disagree with this read.

However, if we knew that he raised too much preflop and called the flop very light, then yes I would agree with bet calling the turn. I'd also agree that we should be value betting thinner than AQ. We don't have that read though.

No 60% is insane. A good opponent will be folding a couple trash hands preflop and a few more on the flop. A more typical opponent will open 100% on the button and fold 0% on the flop.

More talking about 3betting pre. Post is still standard.

If they're that bad then I'd agree with bet call turn. However, the average opening frequency will never reach 100% unless all the players in the pool open 100%. The average folding frequency will never reach 0% unless all the players in the pool fold the flop 0%.

Seriously not trying to troll you but I think this is a pretty bad generalization.

A couple trash hands? I'm thinking more like 19% fold frequency preflop.

A few more on the flop? Even using strict minimum defense frequency, which I think is bad, would have the button folding ~14% on the flop. 86% of 81% is about 70%, not accounting for card removal. Then if we factor in the range vs range advantage that the big blind should have, unless he's playing backwards preflop, and we end up with somewhere between 60% and 70% of all hands that the button should hold on the turn, which is quite far from "any two cards."

Without any reads (including any general player pool reads), BTN should never fold the flop. No, not with T2s even. You are likely playing significantly too tight HU unless you are playing guys who 3bet much less than GTO. Most players are significantly too tight, which is why HU has been a goldmine for an aggressive player.

Those ranges are pretty tight Bob. 81% is certainly on the tight side and it's pretty hard to fold anything on this flop in position getting 7-1.

If he's losing any part of his range it's coming from the top of it (from not raising) not the bottom.

Lol, don't fold hu.

Cepheus opens about 83% and folds this flop 0% fwiw.

Cepheus also bets AQ about 95% on turn in hero's spot.

Ya bet turn, also isn't there a hu forum?

Yeah but it's abandoned.

Bets A7 about 50% too.

Your hand is face up after the turn. I don't mind x/fing river against a good player, given your turn line. That said u should bet turn, especially online b/c villian is peeling a large portion of his range on that flop.

Ok so now that we've established that AQ-A7 are equally profitable as both a bet and a check vs good opponents, can we discuss pure strategies as exploits against the general player population?

I mean I think it's fairly safe to just bet AQ 100% if cepheus is doing it 95%

I don't think that's a safe conclusion.

I thinks a better question you guys shoos be asking is what does your check call range look like on the turn

That's exactly why mixed strategies are used.

Handwaving, probably checking something like A7 through Q9s in my hand ranks, check folding the Q9s/QTs that block backdoor peels, and throw in some traps with hands like KK or decent Jx (not a lot, though, as I'd want to be betting Jx+ the majority of the time).

I think that's why we humans may use mixed strategies for parts of our range, for example when our hands straddle a threshold between raise-call or call-fold.

I think bots are trying to maximize whole strategies (or counterfactual regret minimization in Cepheus' case). Cepheus uses mixed strategies because that gives the best CRM, not because AQ and A7 or any hands that aren't played "purely" share some undisputed equivalence.

I think that using a mixed strategy with AQ-A7 gives Cepheus the best possible regret minimization precisely because the expected values are equal. This guy said it better than I ever could here:

grunch:

amazing flop to triple barrel for value. Honestly even though the jack/king turns are awful for us our hand is still extremely strong. I def triple here for value at least half the time even after the turn J.

As played i'm never folding this spot. We have a lot worse hands in our range that can consider folding. most importantly many offsuit combos

It's a thought.